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 A202502 Modified lower triangular Fibonacci matrix, by antidiagonals. 2
 1, 0, 2, 0, 1, 3, 0, 0, 2, 5, 0, 0, 1, 3, 8, 0, 0, 0, 2, 5, 13, 0, 0, 0, 1, 3, 8, 21, 0, 0, 0, 0, 2, 5, 13, 34, 0, 0, 0, 0, 1, 3, 8, 21, 55, 0, 0, 0, 0, 0, 2, 5, 13, 34, 89, 0, 0, 0, 0, 0, 1, 3, 8, 21, 55, 144, 0, 0, 0, 0, 0, 0, 2, 5, 13, 34, 89, 233, 0, 0, 0, 0, 0, 0, 1, 3, 8, 21, 55 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS This matrix, P, is used to form the Fibonacci self-fission matrix as the product P*Q, where Q is the upper triangular Fibonacci matrix, A202451.  To form P, delete the main diagonal of the transpose of Q. LINKS Clark Kimberling, Fusion, Fission, and Factors, Fib. Q., 52 (2014), 195-202. EXAMPLE Northwest corner: 1...0...0...0...0...0...0...0...0 2...1...0...0...0...0...0...0...0 3...2...1...0...0...0...0...0...0 5...3...2...1...1...0...0...0...0 8...5...3...2...1...1...0...0...0 MATHEMATICA n = 14; Q = NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[Table[Fibonacci[k], {k, 1, n}]]; Qt = Transpose[Q]; P1 = Qt - IdentityMatrix[n]; P = P1[[Range[2, n], Range[1, n]]]; F = P.Q; Flatten[Table[P[[i]][[k + 1 - i]], {k, 1, n - 1}, {i, 1, k}]] (* A202502 as a sequence *) Flatten[Table[Q[[i]][[k + 1 - i]], {k, 1, n - 1}, {i, 1, k}]] (* A202451 as a sequence *) Flatten[Table[F[[i]][[k + 1 - i]], {k, 1, n - 1}, {i, 1, k}]] (* A202503 as a sequence *) TableForm[P]  (* A202502, modified lower triangular Fibonacci matrix *) TableForm[Q] (* A202451, upper tri. Fibonacci matrix *) TableForm[F] (* A202503, Fibonacci self-fission matrix *) CROSSREFS Cf. A202503, A202451, A202452, A202453, A000045. Sequence in context: A062283 A136493 A132213 * A219839 A154312 A236076 Adjacent sequences:  A202499 A202500 A202501 * A202503 A202504 A202505 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Dec 20 2011 STATUS approved

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Last modified March 31 17:36 EDT 2020. Contains 333151 sequences. (Running on oeis4.)